
The average kinetic energy of one molecule of an ideal gas at and 1atm pressure is:
[A]
[B]
[C]
[D]
Answer
508.2k+ views
HINT: The average kinetic energy if dependent only upon the temperature. You can solve this by using the formula- , where the terms have their usual meanings. Do not forget that the Boltzmann constant can be written as- .
COMPLETE STEP BY STEP SOLUTION: We know that the kinetic energy of a particle is the energy that it possesses due to motion. We define it as the work needed to accelerate a body of a certain given mass from rest.
According to the kinetic theory of gases, we can find the average kinetic energy of per molecule any particle by the formula-
Where, is Boltzmann's constant, T is the temperature and K.E is the average kinetic energy.
We can also rewrite the above formula for per mole of a gas as-
Where, n is the number of moles of the particular gas, T is the temperature, R is the universal gas constant whose value is fixed and K.E is the average kinetic energy.
Now, for one molecule of ideal gas, we can write the first formula as-
We know that Boltzmann’s constant
Where, is Avogadro's number.
Now in the question the temperature is given as but we have to convert it in kelvin. We know that is equal to 273 K.
Therefore, is 27 + 273 K = 300K.
The value of the universal gas constant, R = 8.314 J/Kmol
And we know that the value of Avogadro’s number, =
Now we will put these values in the average kinetic energy equation to find out its value for one molecule of an ideal gas.
We can see from the above calculation that the value of average kinetic energy for one molecule of an ideal gas is .
Therefore the correct answer is option [B]
NOTE: The average kinetic energy of a particle is dependent only upon the absolute temperature of the system. The absolute temperature is a scale for measurement of temperature of an object where 0 is taken as absolute zero. The absolute temperature scales are kelvin and Rankine.
COMPLETE STEP BY STEP SOLUTION: We know that the kinetic energy of a particle is the energy that it possesses due to motion. We define it as the work needed to accelerate a body of a certain given mass from rest.
According to the kinetic theory of gases, we can find the average kinetic energy of per molecule any particle by the formula-
Where,
We can also rewrite the above formula for per mole of a gas as-
Where, n is the number of moles of the particular gas, T is the temperature, R is the universal gas constant whose value is fixed and K.E is the average kinetic energy.
Now, for one molecule of ideal gas, we can write the first formula as-
We know that Boltzmann’s constant
Where,
Now in the question the temperature is given as
Therefore,
The value of the universal gas constant, R = 8.314 J/Kmol
And we know that the value of Avogadro’s number,
Now we will put these values in the average kinetic energy equation to find out its value for one molecule of an ideal gas.
We can see from the above calculation that the value of average kinetic energy for one molecule of an ideal gas is
Therefore the correct answer is option [B]
NOTE: The average kinetic energy of a particle is dependent only upon the absolute temperature of the system. The absolute temperature is a scale for measurement of temperature of an object where 0 is taken as absolute zero. The absolute temperature scales are kelvin and Rankine.
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